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It might only be a change of rooms but in the eyes of the law it is a change of property. Particularly because each tenancy agreement should specify the room to which it applies. You need to be sure you have covered everything legally and for this reason it is generally best to get another tenancy agreement signed. It doesn't have to be for a fixed term it could be done as periodic from the beginning.

We would recommend checkout of the old room and checkin to the new room to ensure the deposit is being treated correctly.